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Calculus II

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Unlock your potential with our expertly crafted Calculus 2 notes! Each topic is broken down into clear, step-by-step examples, covering essential techniques like integration methods, applications of integration, sequences and series, and more. Perfect for mastering complex concepts and excelling in...

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  • November 4, 2024
  • 176
  • 2024/2025
  • Class notes
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Cal 2

, be

dx
Area between two curves
ePabley =
f(x
Top

(x)
&




L
↑
gg(y)
y d

a b LEFT
↑
/
↑ dye
1x b
=




X= a bottom Right
- C
y
=




Case 1: To find the area bonded by two functions y =
Lf(y) &


f(x) and y=g(x) on the interval [a,b]
Case 2: To find the area bounded by two functions X=f(y) and X=g(y) on the interval [c,d]


A =


/bRing a AfdTopfly)-gyi

, Area between two curves
Steps
Find the intersection between the curves
Graph
Integrate


Ex1
Graph
3
y = 3 -

x
+y = -

x + 1 Step 2 : Step 3

S2) 1)dx
bottom

Step 1 A =
x +


3 -
x2 = -
X + 1




-
S2
= X2 x 2 - -

= 0

(x 2)(X + D
- = 0
=
-
x*+ x + 2dx
↓
L
.




X= 2 x= -
1

(a, 1) -

(1 2) , "Math 9"

4 .
3 u2

, Area between two curves
- Steps
Find the intersection between the curves
Graph
Integrate =* y
= 2 -x

x =y X= 2 -
y
Ex

y
=
x 22y = 2 -

X Step 2 : Graph x= Vy Step 3 In terms of or In terms ofy dy
dx
Tr (2 4) b

X x2
S (Top-bottom)dx S (Right-left) dy
.




= c -
x
X=
5y y=
A =
A =



x2+ x


:
-
2 =




S2-3)-Ey
(X
S
+ 2)(X -
D = 0
A=
·




↓ A=
(2x- ()
x= 2 X= 1



So g ( 5g)]dy
-




·


+ -




gzt "Math 9"
5u2
& = 4 .




2
4 5,.

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